Question

In a carnival game, you are throwing small balls into 27 cups. How many balls, at minimum, will you need to throw to guarantee that at least one cup has three or more balls?
a) 27
b) 53
c) 54
d) 55

Answer 1

Answer:

d) 55

Step-by-step explanation:

There are 27 cups and we need to find out how many balls need to be tossed into those cups to guarantee that at least one cup has 3 balls

Let's go by worst case scenarios
Pass 1: Toss 27 balls and each ball falls into a different cup so at the end of the first pass each cup has exactly 1 ball in it

Pass 2: Toss another 27 balls and each ball lands in a different cup. This means at the end of pass 2, each cup will have exactly 2 balls in it.

At the end of the two passes each cup has exactly 2 balls in it in the worst case scenario

In the third pass, all you need is one ball since, regardless of which cup the ball lands in, it is guaranteed that one of the cups will have 3 balls

So total number of balls to be tossed to guarantee at least one or more cups has three or more balls
= 27 + 27 + 1 = 55